Ellis is correct, though I want to add a little more about "me and Susan" if that is ok :) If I'm in a casual conversation with a family member or close friend I might say: "me and my friend went to the store earlier". It is not grammatically correct and I'd never say that in writing, but for some reason it just comes up sometimes in speech. I probably would say "my friend and I went to the store earlier" if it was a coworker or acquaintance, if only to sound a little more... Educated maybe? It's interesting how one changes their speech depending on context. When I think about it, there are many occasions I deliberately use less than perfect grammar in my speech so as to not come across as "elite". That said, I don't think that this is as big an issue when English is not one's first language. So I hope that also helps if you hear native speakers use the phrase "me and someone...".

Thank you! That's really helpfull))

It is not an exception to say "me too". A lot of native speakers also get this wrong, myself included. I'm not great with grammatical terms but I will try to explain. I copied this from an article but its a simple way to understand without being too wordy. "The rule for when to use which is actually very simple. Wherever you would say "me" you say "…and me"; wherever you would say "I" you say "…and I." If sentences like this confuse you, try to break them down. 'Susan and I went to the market.' Remove Susan and the sentence becomes 'I went to the market' You don't say 'I and Susan'. Similarly you don't say "Susan and me went to the market" because if you removed Susan from the sentence it becomes 'me went to the market' and that is incorrect. Does this help?

"Me and Susan" is wrong. This is because you would not say "Me go to Thailand". "I and Susan" is also wrong, but only because of word order. We say "Susan and I". This is considered deferential to the other person, and is never reversed. However, you could say "I, with Susan, went ..." although this is perhaps a bit formal or awkward in most circumstances. You can also say "I went with Susan to..." and that would be fine because now Susan is a direct object.